MinT - Best Known (103−30, 103, s)-Nets in Base 3

Best Known (103−30, 103, s)-Nets in Base 3

(103−30, 103, 192)-Net over F₃ — Constructive and digital

Digital (73, 103, 192)-net over F₃, using

3¹ times duplication [i] based on digital (72, 102, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 34, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(103−30, 103, 287)-Net over F₃ — Digital

Digital (73, 103, 287)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−30, 103, 6052)-Net in Base 3 — Upper bound on s

There is no (73, 103, 6053)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 934183 714248 615313 177062 018984 510629 698959 576827 > 3¹⁰³ [i]